Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a more efficient one with contrastive learning. We use graph attention networks and a richer set of features to further improve its performance. Preliminary work. Under review by the International Conference on Machine Learning (ICML). Recently, there has been an increased interest to automate algorithm designs for COPs with machine learning (ML). Many ML approaches learn to either construct or improve solutions within an algorithmic framework, such as greedy search, local search or tree search, for a specific COP, such as the traveling salesman problem (TSP) (Xin et al., 2021; Zheng et al., 2021) , vehicle routing problem (VRP) (Kool et al., 2018) or independent set problem (Li et al., 2018) , and are often not easily applicable to other COPs.